Double-quantitative decision-theoretic rough sets (Dq-DTRS) provide more comprehensive description methods for rough approximations of concepts, which lay foundations for the development of attribute reduction and rule extraction of rough sets. Existing researches on concept approximations of Dq-DTRS pay more attention to the equivalence class of each object in approximating a concept, and calculate concept approximations from the whole data set in a batch. This makes the calculation of approximations time consuming in dynamic data sets. In this paper, we first analyze the variations of equivalence classes, decision classes, conditional probability, internal grade and external grade in dynamic data sets while objects vary sequentially or simultaneously over time. Then we propose the updating mechanisms for the concept approximations of two types of Dq-DTRS models from incremental perspective in dynamic decision information systems with the sequential and batch variations of objects. Meanwhile, we design incremental sequential insertion, sequential deletion, batch insertion, batch deletion algorithms for two Dq-DTRS models. Finally, we present experimental comparisons showing the feasibility and efficiency of the proposed incremental approaches in calculating approximations and the stability of the incremental updating algorithms from the perspective of the runtime under different inserting and deleting ratios and parameter values.

双重定量决策理论粗糙集（Dq-DTRS）为概念的粗糙近似提供了更全面的描述方法，为粗糙集的属性约简和规则提取奠定了基础。现有的Dq-DTRS概念逼近研究在逼近概念时更加关注每个对象的等价类，并从整个数据集中批量计算概念逼近。这使得在动态数据集中计算近似值非常耗时。在本文中，我们首先分析动态数据集中等价类，决策类，条件概率，内部等级和外部等级的变化，而对象随时间顺序或同时变化。然后，从对象的顺序和批次变化的动态决策信息系统中，从增量的角度提出了两种类型的Dq-DTRS模型的概念逼近的更新机制。同时，我们针对两个Dq-DTRS模型设计了增量顺序插入，顺序删除，批处理插入，批处理删除算法。最后，我们进行了实验比较，从不同的插入和删除比率和参数值下的运行时角度，显示了所提出的增量方法在计算近似值时的可行性和效率以及增量更新算法的稳定性。我们为两个Dq-DTRS模型设计了增量顺序插入，顺序删除，批处理插入，批处理删除算法。最后，我们进行了实验比较，从不同的插入和删除比率和参数值下的运行时角度，显示了所提出的增量方法在计算近似值时的可行性和效率以及增量更新算法的稳定性。我们为两个Dq-DTRS模型设计了增量顺序插入，顺序删除，批处理插入，批处理删除算法。最后，我们进行了实验比较，从不同的插入和删除比率和参数值下的运行时角度，显示了所提出的增量方法在计算近似值时的可行性和效率以及增量更新算法的稳定性。